2 matrix problems

[matsu]

Hello!

So pretty please help me with 2 problems. A good guide/link is also much appreciated!

1. There's a matrix

.........5 -1 0
A = ...4 -2 2
........-2 .1 7

Find A<sup>3


So do I multiply the matrix with itself and the result again with the original? A x A = A2; A x A2 = A3</sup>

And the 2nd one, a bit more complicated:

Solve the matrix equation and check if the solution is correct.


.......9 7 6........,,,,,, 2 ..0 .-2
X ....1 1 2 .... =... .18 12 ..9
.......1 1 1 ............24 14 .11

 

[Deleted member 4993]

Hello!

So pretty please help me with 2 problems. A good guide/link is also much appreciated!

1. There's a matrix

.........5 -1 0
A = ...4 -2 2
........-2 .1 7

Find A<sup>3


So do I multiply the matrix with itself and the result again with the original? A x A = A2; A x A2 = A3</sup>


Correct

And the 2nd one, a bit more complicated:

Solve the matrix equation and check if the solution is correct.


.......9 7 6........,,,,,, 2 ..0 .-2
X ....1 1 2 .... =... ..18 12 ...9
.......1 1 1 .............24 14 .11

If you know the process to invert a matrix - the 2 nd problem would be fairly simple.

Let

{X}[A] =

First calculate [A]^-1

then

{X} = * [A]^-1

Where is the identity matrix. Now multiply and solve - and check

 

[matsu]

Thank you for your reply, Subhotosh Khan!

In the 2nd problem, I came up with this:


....1 0 0....1 -1 -6
X. 0 1 0 = 3 0 -9
....0 0 1....5 2 -23

How do I continue from here?

 

[Deleted member 4993]

Thank you for your reply, Subhotosh Khan!

In the 2nd problem, I came up with this:


....1 0 0....1 -1 -6
X. 0 1 0 = 3 0 -9
....0 0 1....5 2 -23

How do I continue from here?

I misinterpreted "X" in the above problem. It cannot be a row or column vector to satisfy the given set of equations. Did the problem provide any other interpretation?

 

[matsu]

I am not sure I follow.. There was no additional info involved if you mean that. Could it be that the matrix I came up with is wrong?

 

[HallsofIvy]

What you have in your last post is X times the identity matrix. What is any matrix times the identity matrix?

 

[matsu]

The same matrix.. So the answer is then


...... .1 -1 -6
X. = 3 0 -9
.... ..5 2 -23

I hope this is the correct answer. Thanks

edit: it does check out!